On classical orthogonal polynomials

Atakishiyev, Natig M.; Rahman, Mizan; Suslov, Sergeĭ K.

doi:10.1007/bf01203415

Cited by 80 publications

(103 citation statements)

References 46 publications

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“…Hahn [2] seems to have been the first to realize that the characterizations of classical orthogonal polynomial sequences based on derivatives and differential equations are too much restrictive [3]. He used a more general operator, the socalled q-difference operator defined by [2,Eq.…”

Section: Introductionmentioning

confidence: 99%

q-Coherent pairs and q-orthogonal polynomials

Area

Godoy

Marcellán

2002

Applied Mathematics and Computation

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In this paper we introduce the concept of q coherent pair of linear functionals. We prove that if ðu 0 ; u 1 Þ is a q coherent pair of linear functionals, then at least one of them has to be a q classical linear functional. Moreover, we present the classification of all q coherent pairs of positive definite linear functionals when u 0 or u 1 is either the little q Jacobi linear functional or the little q Laguerre/Wall linear functional. Finally, by using limit processes, we recover the classification of coherent pairs of linear functionals stated by Meijer. Ó

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Section: Introductionmentioning

confidence: 99%

q-Coherent pairs and q-orthogonal polynomials

Area

Godoy

Marcellán

2002

Applied Mathematics and Computation

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“…Probably the first results in this direction go back to Bochner [3], Favard [5] and Hahn [9]. Moreover, some recent characterizations can be found in [2,6,7], by using either differential operators as Bochner or linear functionals as introduced by Maroni [16,15]. Recently a new characterization of classical continuous, discrete and their q-analogues was given by Verde-Star [21,22] by using a matrix approach.…”

Section: Introductionmentioning

confidence: 99%

Characterizations of classical orthogonal polynomials on quadratic lattices

Sandjon

Branquinho

Foupouagnigni

et al. 2017

Journal of Difference Equations and Applications

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Abstract. This paper is devoted to characterizations classical orthogonal polynomials on quadratic lattices by using a matrix approach. In this form we recover the Hahn, Geronimus, Tricomi and Bochner type characterizations of classical orthogonal polynomials on quadratic lattices. Moreover a new characterization is also presented. From the Bochner type characterization we derive the three-term recurrence relation coefficients for these polynomials.

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“…[3,17]). We also give the relation due to Foupouagnigni et al giving the link between P n and its first associated.…”

Section: Preliminariesmentioning

confidence: 99%

On Factorization and Solutions ofq-difference Equations Satisfied by some Classes of Orthogonal Polynomials

Foupouagnigni

Koepf

Ronveaux

2004

Journal of Difference Equations and Applications

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We derive and factorize the fourth-order q-difference equations satisfied by orthogonal polynomials obtained from some perturbations of the recurrence coefficients of q-classical orthogonal polynomials. These perturbations include the rth associated, the anti-associated, the general co-recursive, co-recursive associated, co-dilated and the general co-modified q-classical orthogonal polynomials. Moreover we find a basis of four linearly independent solutions of these fourth-order q-difference equations and express the modified families in terms of the starting ones.

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On classical orthogonal polynomials

Cited by 80 publications

References 46 publications

q-Coherent pairs and q-orthogonal polynomials

q-Coherent pairs and q-orthogonal polynomials

Characterizations of classical orthogonal polynomials on quadratic lattices

On Factorization and Solutions ofq-difference Equations Satisfied by some Classes of Orthogonal Polynomials

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